论文标题
加冕的多面体和加冕的ANRS
Coronated polyhedra and coronated ANRs
论文作者
论文摘要
所有可分离的可分开的可分开的可分开的空间都在所有可分离的空间中表征为那些接纳Cofinal序列$ K_1 \ subset K_2 \ subset \ subset \ cdots $的空间。由于Petkova的简短序列$ 0 \ to \ lim^1 H^{n-1}（k_i）\ to H^n（x）\ to \ lim h^n（k_i）\至0 $，因此他们的čech共同体被很好地理解了。 我们研究一类双层空间。如果它包含一个compactum $ k $，则我们将其称为“加冕polyhedron”，以使$ x \ setminus k $是多面体，它将称为“加冕polyhedron”。其中包括除了紧凑型和多面体之外，拓扑师的正弦曲线（或Warsaw圆圈）和梳子（=梳子和裂缝）空间等空间。 $ s^n $的每个本地紧凑子集的补充是加冕的多面体。 我们证明，当且仅当它承认可计数的多面体分辨率时，当它是一个可加冕的多面体时，我们证明了一个可分离的空间$ x $。或者，等效地，一个顺序的多面体分辨率$ \ dots \ to r_2 \ to r_1 $。在后一种情况下，我们建立了一个简短的精确顺序$ 0 \ to \ lim^1 h_ {n+1}（r_i）\ to H_n（x）\ to \ lim H_n（r_i）\ to steenrod-sitnikov同源性的同源性，以及（非凡的）同源性的同性恋者$ sapiviative $ scipion $ conteenrod-sitnikov and conteenrod-sitnikov and conteenrod-sitnikov and of-crivisy of-nive。我们还表明，这种同源理论是加冕多面体的强大形状的不变性。另一方面，Quigley的短序列$ 0 \ to \ lim^1π_{n+1}（r_i）\toπ_n（x）\ to \limπ_n（r_i）\ to compacta的steenrod同属compacta的steenrod-sitnikov sitnikov sitnikov同源popy popery popery of Coron of Coroned coroned potorn $ n = 0 $ n = 0 $ n = 0 $ n = 0. 0.
Locally compact separable metrizable spaces are characterized among all metrizable spaces as those that admit a cofinal sequence $K_1\subset K_2\subset\cdots$ of compact subsets. Their Čech cohomology is well-understood due to Petkova's short exact sequence $0\to\lim^1 H^{n-1}(K_i)\to H^n(X)\to\lim H^n(K_i)\to 0$. We study a dual class of spaces. We call a metrizable space $X$ a "coronated polyhedron" if it contains a compactum $K$ such that $X\setminus K$ is a polyhedron. These include, apart from compacta and polyhedra, spaces such as the topologist's sine curve (or the Warsaw circle) and the comb (=comb-and-flea) space. The complement of every locally compact subset of $S^n$ is a coronated polyhedron. We prove that a metrizable space $X$ is a coronated polyhedron if and only if it admits a countable polyhedral resolution; or, equivalently, a sequential polyhedral resolution $\dots\to R_2\to R_1$. In the latter case, we establish a short exact sequence $0\to\lim^1 H_{n+1}(R_i)\to H_n(X)\to\lim H_n(R_i)\to 0$ for Steenrod-Sitnikov homology and also for any (extraordinary) homology theory satisfying Milnor's axioms of map excision and $\prod$-additivity. We also show that such homology theories are invariants of strong shape for coronated polyhedra. On the other hand, Quigley's short exact sequence $0\to\lim^1π_{n+1}(R_i)\toπ_n(X)\to\limπ_n(R_i)\to 0$ for Steenrod homotopy of compacta fails for Steenrod-Sitnikov homotopy of coronated polyhedra, at least when $n=0$.
